Despite the move to save Sears, the company's future is still very much in doubt. An auction of its assets could lead to a decision to start the process of closing down as soon as next week.

Investors assume that JCPenney is well positioned to benefit if Sears stores are forced to close. And there's some justification to that thinking, because there's clear crossover between the shoppers of the two store chains.

An analysis by Cowen and Co. found that 56% of Sears shoppers also shop at JCPenney, the highest overlap of any of the traditional department store chain. For example, the average age of a Sears shopper was nearly 50, according to Coresight. At Penney, it's just over 48.

But not everyone thinks Penney will rise if Sears falls.

"I think it's helpful for Penney if Sears goes away. I don't think it's going to really solve JCPenney's problems," said Neil Saunders, managing director of GlobalData Retail. "I don't think it's a game changer. JCPenney needs to do more to attract shoppers on its own. It's a very telling story if your pathof success relies on someone else's failure. If Sears does die, the spoils of that are going to be widely distributed."

Sears has already closed hundreds of stores in recent years. But JCPenney hasn't been helped by those closures:Itssales have been flat-to-lower in recent years.

"If Penney were really going to benefit from Sears' departure, we would have seen it already," he said. Saunders said.

Penney reported another 3.5% drop in holiday season sales after the market closed Tuesday, which was actually not as bad as feared.

The company also announced it would close three stores, and that it would have positive cash flow for the full fiscal year that ends this month. So shares jumped 9% -- or about 11 cents -- in midday trading Wednesday.

But Penney's decline in sales came as overall holiday sales rose 5.1%, according to an estimate from Mastercard.

And despite the positive cash flow, Penneyis expected to post another net loss for the year.So the company is facing trouble no matter what happens to its longtime rival Sears.

Correction: A previous version of this article misstated the day JCPenney jumped 11%.